select the correct answer.\njessica opened an apparel shop five years ago. in the first year, she made a…

select the correct answer.\njessica opened an apparel shop five years ago. in the first year, she made a profit of $3,125. each year after that, her profit was 20 percent more than in the previous year. what is the total profit jessica earned in 5 years?\n\na. $32,400\nb. $23,255\nc. $7,776\nd. $6,480

select the correct answer.\njessica opened an apparel shop five years ago. in the first year, she made a profit of $3,125. each year after that, her profit was 20 percent more than in the previous year. what is the total profit jessica earned in 5 years?\n\na. $32,400\nb. $23,255\nc. $7,776\nd. $6,480

Answer

Explanation:

Step1: Identify the sequence type

This is a geometric - sequence problem. The first - term $a_1 = 3125$, and the common ratio $r=1 + 0.2=1.2$. The number of terms $n = 5$.

Step2: Use the sum formula for a geometric sequence

The sum formula for a geometric sequence is $S_n=\frac{a_1(1 - r^n)}{1 - r}$. Substitute $a_1 = 3125$, $r = 1.2$, and $n = 5$ into the formula: [ \begin{align*} S_5&=\frac{3125\times(1 - 1.2^5)}{1 - 1.2}\ &=\frac{3125\times(1 - 2.48832)}{- 0.2}\ &=\frac{3125\times(-1.48832)}{-0.2}\ &=\frac{-4651}{-0.2}\ &=23255 \end{align*} ]

Answer:

B. $$23,255$